1. Field of the Invention
The present invention relates to a method and apparatus for dividing an input image into a plurality of images of different frequency bandwidths. More particularly, it relates to a method and apparatus for converting an input frame of image data into a plurality of output frames of image data, the spatial frequency spectrum of each of said plurality of output frames being that of a respective predetermined frequency band of the spatial frequency spectrum of the input frame.
2. Description of the Related Art
It is useful for various processing and transmission techniques to divide an input image into a number of component images each representing a part of the spatial frequency spectrum of the original image. In other words, by converting an input image into a number of component images, each containing the data for only a predetermined bandwidth, and by processing one or more of the component images and then reconstructing an image by summing together all of the component images, the input image can be processed selectively in each of its various bandwidths.
Since it is believed that the human eye has a logarithmic response over the frequency spectrum, it is possible to use a logarithmic array of bandwidths and FIG. 1 of the accompanying drawings illustrates an input frame divided in this manner.
According to FIG. 1, an input frame of data is converted into an output frame which is divided logarithmically into regions of different spatial frequency. With this logarithmic division, the "DC band" (which is a bandwidth starting at zero frequency) has a bandwidth of approximately 1/8th of the source bandwidth in both the horizontal and vertical directions and therefore in each of those directions uses 1/8th of the pixels used in the original source input frame. The bands marked 1 to 9 are AC components of which bands 1, 4 and 7 contain mostly vertically line structures, bands 2, 5 and 8 contain mostly horizontal line structures and bands 3, 6 and 9 contain mostly diagonal line structures.
In practice, an image divided according to FIG. 1 would show a simplified version of the image in the "DC band" area using only 1/64th of the number of pixels. The AC band areas would show separately the additional detail using more pixels (1/16th and 1/4of the number of pixels of the source input image). By adding the higher frequency information of the AC bands to the "DC band", additional detail is added to the simplified image until, with all of the bands added together, the input image is recovered entirely.
FIG. 2 of the accompanying drawings illustrates an apparatus for dividing an input signal into high and low frequency components and then re-combining those components to reform the input signal. This process uses a special filtering arrangement known as a quadrative mirror filter (QMF) bank having the special property of being able to reproduce the output signal as a perfect replica of the input signal. This process of division may be applied to an input image over a number of stages so as to further divide the input image into the frequency bands described with reference to FIG. 1.
As illustrated in FIG. 2, the input signal is simultaneously low pass and high pass filtered and then decimated by removing every other pixel value. Thus, as an example, an input frame could be divided into two halves, each half having half the number of horizontal pixels, one half having the lower half of the frequency spectrum of the input frame and the other half having the higher half.
In reconstruction, the decimated signals are interpolated by first interleaving zero values with the decimated data and then low or high pass filtering the data to reconstruct the interleaved data. The two filtered signals are then summed to reconstruct the original input frame.
FIG. 3 of the accompanying drawings illustrates the frequency spectrum at the various stages of processing of FIG. 2. As illustrated, the decimation process introduces some unwanted alias frequencies and the interpolation mirrors these alias frequencies. However, where the filter banks are designed correctly as a QMF bank, by the following low and high pass filtering and subsequent addition, the unwanted alias frequencies cancel out so that the original input image is reproduced.
Unfortunately, if one of the decimated signals of FIGS. 2 and 3 is further filtered in some way, the symmetry between the aliasing noise of the low and high frequency bands is lost and asymmetric distortion is introduced into the final recombined signal. The problem of asymmetry lies in the process of sub-sampling, since the filters used for decimation are of linear phase.
FIGS. 4a and 4b of the accompanying drawings illustrate the signals created by a 3-stage dimensional wavelet transform from an input square wave with a sampling pitch which is misaligned with the sample decimation structure in order to exercise all sub-sampling phases. The filter bank is constructed from a sequence of QMF filter banks of the type illustrated in FIG. 2. Thus, these figures show a square wave with a pitch ensuring eight different edge faces for odd-tap and even-tap decimation filters respectively.
Both FIG. 4a and FIG. 4b show that the edges of the decimated wave forms have portions where the shape is asymmetric. When these AC component frequencies are subjected to gain changes or non-linear processing, then the effects feed back into the reconstructed signal with asymmetric results. Even-tap filters have no sampling offset in the decimation and reconstruction stages, but nevertheless still show edge distortions as in FIG. 4b.